From XY-plane to UV-plane, Volume of earthworks: Solved CE Board Problems

You may take exams before watching this video: https://mathalino.com/node/18164 Situation. A line on the xy-plane has an equation 5x + 12y = 60. A uv-plane of the same origin has its u-axis rotated at an angle of +arctan (4/3) from the x-axis. (1) Find the uv-coordinates of the y-intercept of the given line. (2) Find the uv-coordinates of the x-intercept of the given line. (3) Find the equation of the given line in the uv-plane. Situation. The following is a set of notes of the earthwork of a road embankment. Sta 5 + 040: 12/-3, -5, 24/-9; Sta 5 + 140: 15/-4.5, -7, 30/-12. If the width of roadway is 12 m and the side slope is 2:1… (1) Determine the volume of earthwork by end area. (2) Determine the volume of earthwork by prismoidal formula. (3) Determine the volume of earthwork by prismoidal correction.